Correlation and Regression PDF

Chapter 3—Correlation and Regression MULTIPLE CHOICE 1. A scatter diagram is a. a bivariate plot of individual data points. b. a univariate plot of individual data points. c. a form of the stem and leaf display. d. a method for calculating variance. ANS: A...

Chapter 3—Correlation and Regression MULTIPLE CHOICE 1. A scatter diagram is a. a bivariate plot of individual data points. b. a univariate plot of individual data points. c. a form of the stem and leaf display. d. a method for calculating variance. ANS: A PTS: 1 REF: The Scatter Diagram 2. Each point on a scatter diagram represents a. the variance of a set of scores. b. the standard deviation of a set of scores. c. where an individual scored compared to the mean. d. where an individual scored on both x and y. ANS: D PTS: 1 REF: The Scatter Diagram 3. Graphs that show pairs of individual values are called ____ plots. a. validity b. regression c. scatter d. normality ANS: C PTS: 1 REF: The Scatter Diagram 4. What do scatter diagrams do? a. Allow visualization of the relationship between two variables b. Create an objective measure of reliability c. Relate univariate observations to bivariate distributions d. Demonstrate the statistical validity of measures ANS: A PTS: 1 REF: The Scatter Diagram 5. If the line that comes closest to all points in a scatter diagram is perfectly straight, the correlation between the two variables is a. linear. b. curvilinear. c. positive. d. unknown. ANS: A PTS: 1 REF: Correlation 6. The observation that Y decreases as X increases suggests a. a positive correlation. b. no correlation. c. a negative correlation. d. a curvilinear correlation.  ANS: C PTS: 1 REF: Correlation 7. In a negative correlation, a. individuals tend to maintain the same or a similar relative performance. b. scores on one variable tell us nothing about scores on a second. c. individuals who score low on one variable tend to score low on a second. d. high scores on the X variable are associated with low scores on the Y variable. ANS: D PTS: 1 REF: Correlation 8. The correlation equals +1 for which of the following four pairs of numbers? a. (2, 4), (4, 8), (0, 0), (-2, -4) b. (0, 0), (1, 1), (2, 4), (3, 9) c. (4, 3), (2, -1), (-2, -9), (0, -5) d. (4, -9), (2, -1), (-2, -2), (0, -5) ANS: A PTS: 1 REF: Correlation MSC: www 9. The correlation equals -1 for which of the following four pairs of numbers? a. (2, 4), (4, 8), (0, 0), (-2, -4) b. (0, 0), (1, 1), (2, 4), (3, 9) c. (4, 3), (2, -1), (-2, -9), (0, -5) d. (4, -9), (2, -1), (-2, -2), (0, -5) ANS: C PTS: 1 REF: Correlation 10. Correlation coefficients describe the a. degree of linearity of relation between X and Y. b. mean of X and Y. c. direction and magnitude of relationship between X and Y. d. causality of relationships between X and Y. ANS: C PTS: 1 REF: Correlation 11. People who drink caffeinated beverages tend to experience increased alertness and psychomotor activity. This demonstrates a(n) a. positive correlation. b. negative correlation. c. zero correlation. d. unknown. ANS: A PTS: 1 REF: Correlation 12. Which of the following correlations represents the strongest relationship between two variables? a. -.85 b..01 c..50 d..80 ANS: A PTS: 1 REF: Correlation 13. Given the following ordered pairs, the correlation is 87 76 32 12 12 a. positive. b. negative. c. zero. d. perfect. ANS: A PTS: 1 REF: Correlation 14. If the scores on X give us no information about the scores on Y, this indicates a. a positive correlation. b. a negative correlation. c. no correlation. d. curvilinear correlation. ANS: C PTS: 1 REF: Correlation 15. Which of the following four pairs of numbers describes a nonlinear relation? a. (2, 4), (4, 8), (0, 0), (-2, -4) b. (0, 0), (1, 1), (2, 4), (3, 9) c. (4, 3), (2, -1), (-2, -9), (0, -5) d. (4, -9), (2, -1), (-2, -2), (0, -5) ANS: B PTS: 1 REF: Correlation 16. Which of the following four pairs of numbers describes a correlation that is very close to.0? a. (2, 4), (4, 8), (0, 0), (-2, -4) b. (0, 0), (1, 1), (2, 4), (3, 9) c. (4, 3), (2, -1), (-2, -9), (0, -5) d. (4, -9), (2, -1), (-2, -2), (0, -5) ANS: D PTS: 1 REF: Correlation 17. Which of the following is true of correlations? a. They cannot be used to determine statistical significance. b. They provide the basis for transforming observations to scales. c. They are particularly useful with nominal scales. d. They describe the direction and magnitude of relationships between two variables.  ANS: D PTS: 1 REF: Correlation 18. The best-fitting straight line through a set of points in a scatter diagram is known as the a. regression line. b. linear line. c. correlation line. d. perfect correlation. ANS: A PTS: 1 REF: Regression 19. What is the point of least squares for the numbers 4, 6, 8, and 10? a. indeterminate b. 4 c. 7 d. 10 ANS: C PTS: 1 REF: Regression MSC: www 20. What is the point of least squares for the numbers 2, 7, 8, and 11? a. indeterminate b. 4 c. 7 d. 10 ANS: C PTS: 1 REF: Regression 21. Suppose that X and Y are uncorrelated. X has a mean of 15 and Y has a mean of 19. Given a score of 14 on a particular X observation, the best prediction of Y is a. 0. b. 15. c. 19. d. indeterminate. ANS: C PTS: 1 REF: Regression 22. Suppose that X is used to predict Y and that both are in Z-score form. Which of the following is always true regarding the predicted Y score? a. It is larger than the obtained X score. b. It is smaller than the X score. c. It is closer to 0 than the obtained Y score. d. It is closer to 0 than the X score. ANS: D PTS: 1 REF: Regression 23. A common use of correlation is to determine evidence for a. criterion validity. b. face validity. c. a normative sample.  d. a scatter plot. ANS: A PTS: 1 REF: Regression 24. In the linear equation Y´ = a + bX, "a" is called a. the regression coefficient. b. the intercept. c. the actual score. d. the predicted score. ANS: B PTS: 1 REF: Regression 25. When you know nothing about a person's academic ability, the best estimate of his or her academic ability should be based on the a. mean. b. Z score. c. criterion. d. correlation. ANS: A PTS: 1 REF: Regression 26. In the linear equation Y´ = a + bX, "b" is called a. the slope. b. the intercept. c. the actual score. d. the predicted score. ANS: A PTS: 1 REF: Regression 27. In the formula Y´ = a + bX, Y´ is the a. regression coefficient. b. raw score of Y. c. predicted value of Y. d. intercept. ANS: C PTS: 1 REF: Regression 28. The point at which the regression line crosses the Y axis is the a. slope. b. regression coefficient. c. predicted value of X. d. intercept. ANS: D PTS: 1 REF: Regression 29. The intercept is the a. value obtained using the equation to predict scores.  b. slope of the regression line. c. value of Y when X is zero. d. standard deviation of a test score. ANS: C PTS: 1 REF: Regression 30. Suppose that we find a regression relating X to Y by the following equation: Y´ = 12 +.80X. If we observe an X score of 2, what score on Y would we expect? a. 8 b. 10.4 c. 13.6 d. 16.4 ANS: C PTS: 1 REF: Regression 31. The difference between the observed and predicted score is a. the residual. b. the intercept. c. the Z score. d. correlation coefficient. ANS: A PTS: 1 REF: Regression 32. What is the difference between correlation and regression? a. Regression requires standardized units, while correlation does not. b. Correlation is the same thing as regression except that the scores are in standardized units. c. In regression, scores on the Y axis regress toward the mean, while in correlation they do not. d. In correlation, scores on the Y axis regress toward the mean, while in regression they do not. ANS: B PTS: 1 REF: Regression 33. The correlation coefficient can take any value from a. -1.0 to 1.0. b. 0 to 1.0. c. -1.0 to 0. d. 1.0 to 10.0. ANS: A PTS: 1 REF: Regression 34. A correlation of.80 suggests that a. the scores on X and Y are not related. b. standardized scores on the Y axis are expected to be.8 times the corresponding scores on the X axis.  c. scores on Y will be 80% larger than corresponding scores on X. d. the differences between X and Y are statistically non-significant. ANS: B PTS: 1 REF: Regression 35. If the correlation between X and Y is 0 and we observe a score (in Z units) of 1.5 on X, what score would be predicted for Y? a. -1.5 b. -.75 c. 0 d. 1.5 ANS: C PTS: 1 REF: Regression 36. If the correlation between X and Y is.60 and we observe a score of 1.0 (Z units) on X, what score would be predicted for Y? a. -1.2 b. 0 c. 0.6 d. 1.6 ANS: C PTS: 1 REF: Regression 37. Correlation coefficients can be tested for significance using the a. Z distribution. b. t distribution. c. principle of least squares. d. regression distribution. ANS: B PTS: 1 REF: Regression 38. Assumed that X and Y correlate.3 in a sample of 102. What is the approximate t-value used to test the significance of this relationship? a. 0 b. 1 c. 2 d. 3 ANS: D PTS: 1 REF: Regression 39. Assume that X and Y correlate.6, are in Z score form, and that a particular value of X is 1. What is the predicted value of Y? a. 0 b..4 c..6 d. 1 ANS: C PTS: 1 REF: Regression 40. Assume that X and Y correlate.4, are in Z score form, and that a particular value of X is 1. What is the predicted value of Y? a. 0 b..4 c..6 d. 1 ANS: B PTS: 1 REF: Regression 41. If the regression between X and Y is less than perfect, a. predicted values of Y are relatively further from the mean of Y than observed values of X are to the mean of X. b. predicted values of Y are relatively closer to the mean of Y than observed values of X are to the mean of X. c. values of Y cannot be predicted from observations of X. d. observed values of X are relatively closer to the mean of X than predicted values of Y are to the mean of Y. ANS: B PTS: 1 REF: Regression 42. In regression plots, a perfect forecaster of the criterion is at a(n) a. 45 degree angle. b. 90 degree angle. c. 0 degree angle. d. 100 degree angle. ANS: A PTS: 1 REF: Regression 43. What does regression do? a. It ensures the statistical significance of correlations. b. It converts raw scores to t scores. c. It makes predictions about scores based on other scores. d. It creates linear relationships for transforms. ANS: C PTS: 1 REF: Regression 44. Which of the following is the slope of the regression line? a. The regression coefficient b. The intercept c. The relative covariance d. The best fit ANS: A PTS: 1 REF: Regression 45. Which of the following is true of the best-fitting line? a. It establishes statistical significance. b. It increases as the correlation decreases. c. It is rarely useful for prediction. d. It minimizes residuals.  ANS: D PTS: 1 REF: Regression 46. Which of the following is used to test the statistical significance of correlations? a. The regression line b. The t distribution c. The coefficient of relatedness d. The slope and intercept ANS: B PTS: 1 REF: Regression 47. What type of prediction uses information gained from representative groups? a. normative b. regressive c. correlational d. transformative ANS: A PTS: 1 REF: Regression 48. Which of the following is a true dichotomous variable? a. football players' numbers b. weight c. time d. gender ANS: D PTS: 1 REF: Other Correlation Coefficients 49. An appropriate correlation coefficient describing the relationship between two artificially dichotomous variables is a. biserial correlation. b. phi coefficient. c. tetrachoric correlation. d. point biserial correlation. ANS: C PTS: 1 REF: Other Correlation Coefficients MSC: www 50. To assess the relationship between intelligence and passing or failing this exam, you would use the a. point biserial. b. Pearson r. c. biserial correlation. d. tetrachoric correlation. ANS: A PTS: 1 REF: Other Correlation Coefficients 51. Which of the following is an artificially dichotomous variable? a. gender b. weight c. passing/failing a final exam d. GPA ANS: C PTS: 1 REF: Other Correlation Coefficients 52. One formula for the correlation between two dichotomous variables is a. Spearman’s rank order formula. b. the point biserial correlation. c. the phi coefficient. d. the biserial correlation. ANS: C PTS: 1 REF: Other Correlation Coefficients 53. One formula for the correlation between a continuous variable and an artificially dichotomized variable is a. Spearman’s rank order formula. b. the point biserial correlation. c. the phi coefficient. d. the biserial correlation. ANS: D PTS: 1 REF: Other Correlation Coefficients 54. The type of correlation coefficient used to find the association between two sets of ranks is called a. Spearman’s rho. b. the point biserial correlation. c. the phi coefficient. d. factor loading. ANS: A PTS: 1 REF: Other Correlation Coefficients 55. In order to determine the relationship between sex of subject and income level, one would use the a. phi coefficient. b. point biserial correlation. c. Spearman's rho. d. Pearson r. ANS: B PTS: 1 REF: Other Correlation Coefficients 56. Which of the following describes the relationship between a true dichotomous variable and a continuous variable? a. Spearman’s rho b. point biserial correlation  c. Pearson product-moment d. the phi coefficient ANS: B PTS: 1 REF: Other Correlation Coefficients 57. Which of the following is used to describe the relationship between two dichotomous variables, at least one of which is a true dichotomy? a. tetrachoric correlation b. phi coefficient c. point biserial correlation d. Spearman’s rho ANS: B PTS: 1 REF: Other Correlation Coefficients 58. Which of the following describes the relationship between two artificially dichotomous variables? a. tetrachoric correlation b. factor analysis c. discriminant analysis d. multiple regression ANS: A PTS: 1 REF: Other Correlation Coefficients 59. The type of correlation coefficient used to correlate a dichotomous variable (two categories) and a continuous variable is called a. Spearman’s rho. b. the point biserial correlation. c. the phi coefficient. d. multivariate analysis. ANS: B PTS: 1 REF: Other Correlation Coefficients 60. The difference between the predicted value of Y and the observed value is called the a. standard deviation. b. standard error of the mean. c. residual. d. factor score. ANS: C PTS: 1 REF: Terms and Issues in the Use of Correlation 61. The formula Y - Y´ represents a. the true score. b. the residual. c. the standard error of estimate. d. shrinkage. ANS: B PTS: 1 REF: Terms and Issues in the Use of Correlation 62. X and Y correlate.5. What is the coefficient of determination of this relation? a. 0 b..25 c..50 d..75 ANS: B PTS: 1 REF: Terms and Issues in the Use of Correlation 63. X and Y correlate.2. What is the coefficient of determination of this relation? a. 0 b..04 c..45 d..75 ANS: B PTS: 1 REF: Terms and Issues in the Use of Correlation 64. The coefficient of determination is the a. number of degrees of freedom. b. difference between predicted and observed values of Y. c. mean. d. squared correlation coefficient. ANS: D PTS: 1 REF: Terms and Issues in the Use of Correlation 65. X and Y correlate.6. What is the coefficient of alienation of this relation? a. 0 b..36 c..60 d..80 ANS: D PTS: 1 REF: Terms and Issues in the Use of Correlation 66. X and Y correlate.8. What is the coefficient of alienation of this relation? a. 0 b..20 c..60 d..80 ANS: C PTS: 1 REF: Terms and Issues in the Use of Correlation 67. The standard deviation of the residuals is called the a. coefficient of alienation. b. shrinkage. c. coefficient of determination. d. standard error of estimate. ANS: D PTS: 1 REF: Terms and Issues in the Use of Correlation 68. The amount of decrease observed when a regression equation is created for one population and applied to another is called a. the true score. b. the standard deviation.  c. a residual. d. shrinkage. ANS: D PTS: 1 REF: Terms and Issues in the Use of Correlation 69. The observation that the preference for watching TV shows depicting violence is correlated -.86 with altruism suggests a. TV violence causes altruistic behavior. b. altruistic behavior causes a preference for TV violence. c. increases in altruism are associated with decreases in preference for violent programs. d. there is no relationship between TV preference and altruism. ANS: C PTS: 1 REF: Terms and Issues in the Use of Correlation 70. The coefficient of alienation is the a. squared correlation coefficient. b. index of variation in Y not explained by its relationship to X. c. standard deviation of the residuals. d. square root of the standard deviation. ANS: B PTS: 1 REF: Terms and Issues in the Use of Correlation 71. Assume that X and Y correlate.6, are in Z-score form, and that a particular value of X is 1. What is the value of the Y residual? a. 0 b..4 c..6 d. 1 ANS: B PTS: 1 REF: Terms and Issues in the Use of Correlation 72. What is the sum of the predicted value of Y and its residual? a. the coefficient of determination b. the obtained Y c. the alienation coefficient d. the sum of squares ANS: B PTS: 1 REF: Terms and Issues in the Use of Correlation 73. A regression equation was derived from a small sample in which X and Y correlated.6. The equation is Y´ = 6X + 15. Suppose this equation were applied to a second sample. It is likely that the correlation between the scores predicted from this equation and the observed scores will be a. 0. b. less than 0.6. c. approximately 0.6. d. greater than 0.6. ANS: B PTS: 1 REF: Terms and Issues in the Use of Correlation MSC: www 74. It is difficult to observe significant correlation between the GRE score and graduate school GPA among elite graduate students because of a. range restriction. b. the elite syndrome. c. unreliability in the GRE. d. shrinkage. ANS: A PTS: 1 REF: Terms and Issues in the Use of Correlation 75. The relationship between TV viewing and aggressive behavior might be influenced by poor social adjustment. Social adjustment here is regarded as a(n) ____ problem. a. restricted range b. shrinkage c. third variable d. lack of linearity ANS: C PTS: 1 REF: Terms and Issues in the Use of Correlation 76. A study demonstrates that the number of cigarettes smoked per day is significantly correlated with the number of respiratory infections experienced by young adults. This observation suggests that a. cigarette smoking causes respiratory infections. b. cigarette smoking does not cause respiratory infections. c. cigarette smoking causes some respiratory infections but not others. d. the data do not allow inferences about causation. ANS: D PTS: 1 REF: Terms and Issues in the Use of Correlation 77. A correlation was of.6 was obtained from a particular sample. The two measures are then administered to a sample from more homogeneous population. The expected correlation in this new sample will probably be a. 0. b. less than.6. c. approximately.6. d. greater than.6. ANS: B PTS: 1 REF: Terms and Issues in the Use of Correlation 78. If the coefficient of determination is 0.49, what is the correlation coefficient? a. 0.24 b. 0.51 c. 0.70 d. 0.89 ANS: C PTS: 1 REF: Terms and Issues in the Use of Correlation 79. An appropriate statistical technique that one might use to see how Scholastic Aptitude Test Scores and High School Grades jointly relate to Freshman grades is a. linear regression. b. multiple regression. c. discriminant analysis. d. factor analysis.  ANS: B PTS: 1 REF: Multivariate Analysis 80. An appropriate statistical technique that one might use to see how Scholastic Aptitude Test Scores and High School Grades explain differences among majors in Psychology, Sociology, and Political Science is a. linear regression. b. multiple regression. c. discriminant analysis. d. factor analysis. ANS: C PTS: 1 REF: Multivariate Analysis MSC: www 81. Suppose you had a series of eight measures of anxiety that you administered to a sample. You would use the statistical technique referred to as ____ in order to test the hypothesis that they are all measuring the same thing (anxiety). a. linear regression b. multiple regression c. discriminant analysis d. factor analysis ANS: D PTS: 1 REF: Multivariate Analysis 82. Suppose we wanted to predict success in graduate school on the basis of undergraduate G.P.A., IQ, and professor ratings. The statistical method that would be most useful is a. bivariate correlation. b. Spearman’s rho. c. multiple regression. d. factor analysis. ANS: C PTS: 1 REF: Multivariate Analysis 83. How is discriminant analysis different from multiple regression? a. In discriminant analysis, the criterion variable is a set of categories rather than a continuous variable. b. The criterion variable is continuous in discriminant analysis but not in multiple regression. c. Discriminant analysis is a form of factor analysis, while multiple regression is not. d. Discriminant analysis and multiple regression involve exactly the same process. ANS: A PTS: 1 REF: Multivariate Analysis 84. Principle components are found in a. multiple regression. b. factor analysis. c. discriminant analysis. d. Spearman's rho. ANS: B PTS: 1 REF: Multivariate Analysis 85. A factor loading is a. a residual.  b. the correlation between two principle components. c. the correlation between an item and a factor. d. the square root of a factor. ANS: C PTS: 1 REF: Multivariate Analysis 86. The primary purpose of a factor analysis is to a. determine the relationship between variables. b. reduce a larger set of variables to a smaller composite set. c. insure that proper inferences are being made. d. determine the degree of non-association between variables. ANS: B PTS: 1 REF: Multivariate Analysis 87. In order to examine the relationship between gender, hair color, and intelligence, you would use a. the Pearson r. b. multivariate analysis. c. the phi coefficient. d. the tetrachoric correlation. ANS: B PTS: 1 REF: Multivariate Analysis ESSAY 1. Identify and discuss the use of two measures of correlation other than the Pearson r. ANS: Answer not provided. PTS: 1 REF: Other Correlation Coefficients 2. Explain the correlation-causation problem and give an example. ANS: Answer not provided. PTS: 1 REF: Terms and Issues in the Use of Correlation 3. It is frequently argued that the Scholastic Aptitude Test (SAT) should not be used to select students because the correlation between their SAT scores and their freshman grades may be low, indicating that the SAT is not a valid measure. How does the concept of range restriction apply here? What other factors might operate to reduce this correlation? ANS: Answer not provided. PTS: 1 REF: Terms and Issues in the Use of Correlation 4. Compare and contrast shrinkage and restriction of range. ANS: Answer not provided. PTS: 1 REF: Terms and Issues in the Use of Correlation